For position determination, global or satellite-based positioning systems GNSS (e.g. GPS, GLONASS, GALILEO, etc.) are currently being used for many applications and will be in the future. For this purpose, the satellites of the space segment emit electromagnetic radiation at a plurality of carrier frequencies. In general, one or more codes which serve for the transmission of data are superposed on these carrier frequencies by modulation.
The electromagnetic radiation is detected by a receiver and evaluated with regard to different variables for position determination. Thus, on the basis of the transit times of the signals from a satellite to the receiver, so-called pseudo-paths are determined, these deviating from the true distance owing to various influences, such as, for example, owing to the difference between true system time and the respective representations in the satellite and receiver clocks. These pseudo-path measurements are based on the code which is superposed on a carrier frequency by modulation and contains data about the time of emission of the signal by the satellite. The satellite signals are transmitted at a plurality of carrier frequencies which are designated, for example for the GPS system, by L1 (154·10.23·106 Hz), L2 (120·10.23·106 Hz) or L5 (115·10.23·106 Hz). In the case of GALILEO, for example, the corresponding frequencies are designated as E1-L1-E2 and E5a (L5), E6 at (125·10.23·106 Hz) being available as a third signal. Other frequencies can likewise be measured in the case of GALILEO.
A further possibility for distance determination consists in the use of carrier phase data of the signals. The measurement of the phase shift is carried out, the use of the carrier phases permitting a precise position determination. However, the disadvantage of the phase measurements is that their distance is determined only to a multiple of the wavelength used, which is designated as phase ambiguity. If these phase ambiguities were known, so-called phase paths as highly accurate equivalents to the pseudo-paths would have been available —based on the carrier phases. Phase paths are obtained by multiplication of the observations with the aid of the carrier phases in cycles with the wavelength applicable in each case.
By utilizing two frequencies, it was originally intended to correct ionospheric transit time delays, but special combination phases can also be generated by linear combinations, such as, for example, ionosphere- or geometry-free linear combinations. Such linear combinations, i.e. in general a summation of any desired multiples of n elements xi to be combined, i.e.
                    x        =                              ∑                          i              =              1                        n                    ⁢                                          ⁢                                    a              i                        ⁢                          x              i                                                          (        0        )            with the associated positive or negative coefficients ai and optionally additive terms independent of the elements, may be generated for pseudo paths as well as observations of the carrier phases, i.e. the phase paths. For this purpose, the corresponding observations are multiplied by certain factors. For generating a geometry- or ionosphere-free linear combination, real-value factors are used. The real-value factors destroy the integral nature of the phase ambiguity for the exact determination in an algorithm. If integral factors are used in the linear combinations, the integral nature is retained for the determination within an algorithm.
The combination of carrier phases and pseudo-paths at both wavelengths for resolving so-called “wide lanes” was developed in the 1980s. A first, civil GPS receiver with pseudo-path measurement at both frequencies was on the market at that time. This receiver used the still unencrypted P-code, both at the L1 frequency and at the L2 frequency. The measured pseudo-paths were substantially more accurate than pseudo-path measurements with the aid of the C/A code (300 m wavelength), owing to the shorter code wavelength of about 30 metres. L1 and L2 pseudo-paths as well as L1 and L2 carrier phase measurements were recorded. In the case of the “wide lanes”, only integral factors are used and hence the possibility of the advantageous determination of integral phase ambiguities is retained.
The principle of the combination of the observations of two frequencies consists in the elimination of the terms common to all observations, combinations of oblique paths to the satellite, troposphere and the like and of the dispersive, ionospheric term which has a different sign for pseudo-paths and phase measurements. While in general resolution is effected only for the advantageous wide lane, the method can be set up for any desired linear combinations of two frequencies. It should be noted here that the resolution of the wide lanes between a station and a satellite is possible only in theory. Between the frequencies, different clock errors in the satellite and the receiver hinder this possibility. For this reason, a resolution can be effected only after the formation of so-called double differences between two satellites and two receivers or the introduction of the respective clock differences.
This approach of using two frequencies and the measurements of the coordinated carrier phases and pseudo-paths combines the accuracy possible in principle with the carrier phase with the determination of the phase ambiguity, which is possible by the pseudo-path measurement. The so-called Melbourne-Wübbena approach, in which phase and pseudo-path measurement are combined in a system of equations to be solved permits a direct resolution. Here, the carrier phase measurements are stated as phase paths, i.e. in metric units instead of cycles otherwise usually used—the so-called phase path is obtained by multiplication with the wavelength of the respective carrier phase.
Another approach is based on the modeling of the phase paths for the two carrier frequencies according to
                              ϕ          1                =                  ρ          -                      I                          f              1              2                                +                                    N              1                        ⁢                          λ              1                                +                      ɛ                          ϕ              1                                                          (        1        )                                          ϕ          2                =                  ρ          -                      I                          f              2              2                                +                                    N              2                        ⁢                          λ              2                                +                      ɛ                          ϕ              2                                                          (        2        )            and the pseudo-paths according to
                              R          1                =                  ρ          +                      I                          f              1              2                                +                      ɛ                          R              1                                                          (        3        )                                          R          2                =                  ρ          +                      I                          f              2              2                                +                      ɛ                          R              2                                                          (        4        )            where, with i=1,2, φi designates a phase path coordinated with the i th carrier frequency, Ri designates the i th pseudo-path, ρ designates the geometric path between satellite and receiving unit, in particular including clock errors and non-dispersive error terms, I/fi2 designates an ionospheric influence for the i th carrier frequency, Ni designates a phase ambiguity for the wavelength λi coordinated with the i th carrier frequency, εφi designates a noise term for the phase path coordinated with i th carrier frequency and εRi designates a noise term for the i th pseudo-path. The solution of a corresponding system of equations includes the determination of the phase ambiguities Ni or a linear combination
      G    ⁡          (              N        i            )        =      A    +                  ∑                  i          =          n                n            ⁢                          ⁢                        b          i                ⁢                  N          i                    of the phase ambiguities Ni with a term A independent of the phase ambiguities so that a corresponding position determination is possible.
The direct, numerical combination of these four observations permits the resolution of the ambiguities of the difference between the two carrier phase measurements. Under certain circumstances, the results must be accumulated over a certain time in order to permit a unique resolution, i.e. the mean value of the calculated wide lanes is determined. This is because the pseudo-path measurements are generally too inaccurate. Another possibility consists in the use of a Kalman filter in which the observations are modeled in the simplest manner. Use of filters is explained, for example, in Euler, Hans-Jürgen and Goad, Clyde C., “On optimal filtering of GPS dual frequency observations without using orbit information”, Bulletin Géodésique (1991) 65:130-143.
All these methods constitute a method for pre-processing the observations, i.e. the pseudo-paths and phase paths, these generally being used for the convergence of phase ambiguities. In general, these methods can be applied to raw undifferentiated observations or all differences described in the literature, such as double differences. If raw observations or a small differentiation level are used as the customary double difference between receivers and satellites, phase ambiguities in a double difference must be determined for a precise, differential position determination, since these integral values can be determined only in the double difference. This is necessary owing to still existing errors, for example satellite and receiver clock errors. By the combination of two carrier phase measurements, which are expressed as phase paths in equations (1) and (2), and the two pseudo-path measurements in equations (3) and (4) with subsequent double differentiation, the phase ambiguities can be determined and specified for widelanes without inclusion of the geometry, i.e. calculation of the position of the satellites and of the receiver. Here, the advantage of the widelane lies in this method. There, and as long as two identical satellites at two arbitrary locations are visible, the fixing can be carried out without actual determination of only locally correlating variables.
By using the two frequencies for the common derivation of all phase paths and pseudo-paths, the achievable accuracy is in principle limited to the two frequencies. An independent improvement or optimization of phase path or pseudo-path measurement cannot be performed. In addition carrier frequencies which are both coded and can be evaluated with respect to their phases with required accuracy are always required.
Owing to the observation types available in the system, corresponding methods of the prior art are always based on identical frequencies for pseudo-paths and phase paths. With the advent of discussions on extended or new satellite positioning systems and the greater number of available measurement frequencies, further methods were developed which in each case use pseudo-paths and phase paths of the frequencies appropriate in each case, i.e. always both these distance data.
A three-frequency method of the prior art is described, for example, in Vollath et al., “Analysis of Three-Carrier Ambiguity Resolution Technique for Precise Relative Position in GNSS-2”, Navigation, Inst. of Nav., vol. 46, no. 1, pages 13-23. In this method, observations of three frequencies with the indices 1, 2 and 4 are used simultaneously for pseudo-paths and phase paths. The approach aims at splitting into geometry- and ionosphere-free multi-frequency solutions but always uses both variables measured per carrier frequency, i.e. pseudo-path and carrier phase.
US 2005/0080568 describes a method for resolving phase ambiguities, in which three GPS frequencies are likewise used. Here too pseudo-paths corresponding to the respective phase observations are always used.
A similar approach with phase paths and pseudo-paths based on identical frequencies is described in Jung et al., “Optimization of Cascade Integer Resolution with Three Civil Frequencies”, Proceedings of the Inst. of Nav., 19.09.2000.